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Упражнение 5

Основные действия арифметики: basic operations of arithmetic

 

Действие сложения, вычитания, умножения, деления: operations of addition, subtraction, multiplication and division.

 

В результате этой операции (действия): as a result of this operation

 

Слагаемое – addend ['xdend],

сумма - sum,

уменьшаемое – minuend ['mInjVend],

вычитаемое – subtrahend ["sAbtrq'hend],

разность - difference,

множимое – multiplicand ["mAltIplI'kxnd],

множитель – multiplier ['mAltIplaIq],

произведение - product,

делимое – dividend ['dIvI|dend, -dqnd],

делитель – divisor [dI'vaIzq],

частное – quotient ['kwqVS(q)nt],

остаток – remainder [rI'meIndq].

 

То же самое можно сказать о…: the same may be said about

 

обратная операция: inverse operation

 

каждое из них называется сомножителем: each of them is called a factor.

 

это число не содержится целое число раз в…this number is not contained a whole number of times in

 

коммутивный, ассоциативный, распределительный законы:

commutative, associative, distributive laws.

 

 

Упражнение 6

Найдите в тексте антонимы следующих слов:

Addition - subtraction,

multiplication – division,

sum – difference,

product - fraction,

to add – to subtract,

to multiply – to divide,

identical - different,

different - identical,

fraction – integer, product,

meaningful - meaningless,

unimportant – meaningful.

 

 

Упражнение 7

Переведите следующие предложения на русский язык

1. The patient is being examined now. Keep silent.
2. A new grammar rule is being explained.
3. When I entered the hall the lecture was being listened to with great attention.
4. The prizes have already been distributed.
5. Don’t worry. The sick child has just been taken to hospital.
6. The driver had already been sent for by that time.
7. All copies of Moscow News had been sold out by half past nine.
8. Be sure, letters and newspapers will have been brought by ten.
9. The latest news was being listened to when Mike came in.
10. The new performance has been much spoken about of late.

 

 

Упражнение 8

1) The sum of 2 numbers is 15. If 2 is added to the first number and the sum multiplied by 3, the product is 11 more than 7 times the second. Find the numbers.

 Сумма двух чисел равна 15. Если прибавить 2 к первому числу и умножить сумму на 3, то результат будет на 11 больше второго числа, умноженного на 7.

 

(x+ 2)*3 = 7y + 11

x + y = 15

 

Ответ: x = 11, y = 4

 

2) What happens with the sum if one of the addends becomes some units greater (less)?

Что будет с суммой, если одно из слагаемых станет не несколько единиц больше (меньше)?

 

The sum will become some unites greater (less).

Сумма станет на несколько единиц больше (меньше)

 

 

3) Write down the number which is 2 less than three times X.

Напишите число, которое на 2 меньше, чем Х.

Если Х = 10, тогда 3*10 – 2 = 28

Если Х = х (переменная), тогда 3х – 2.

 

 

 

4) Find the number such that when it is doubled and 6 added, the result is the same as when the number is trebled (утроить) and 2 subtracted.

Найти такое число, что если его удвоить и к произведению прибавить 6, то результат окажется равным разности исходного числа, умноженного на 3, и 2. 

 

2x + 6 = 3x -2

 

Ответ: х = 8

 

5) Find the number which is as much greater than 25 as it is less than 93.

Найдите число, которое на столько больше 25, на сколько меньше 93.

 

x + 25 = 93 - х

х = 34

 

Число = 25 + 34 = 59

 

Ответ: 59

 

 

6) The number which is 5 more than X is 6 times as big as the number which is 5 less than X. Find X.

Число, большее Х на 5, в 6 раз больше числа, которое меньше Х на 5.

 

(x + 5)/6 = x - 5

 

Ответ: х = 7

 

7) Write down the three consecutive integers of which "d” is the middle one (the smallest, the greatest).

Напишите три последовательных целых числа, где "d” – средний элемент.

3, 4, 5

 

 

Упражнение 9.

Расположите следующие предложения в логической последовательности.

I

1. Subtraction is the process of finding the difference between 2 numbers by taking the smaller of the two from the larger.
2. In order to find the remainder the subtrahend is written under the minuend as in addition.
3. When the process is completed the third complete number below the subtrahend is the desired remainder.
4. The number which is subtracted is called the subtrahend, the other number is called the minuend and their difference, the number which remains after the subtrahend is subtracted from the minuend is called the remainder.
5. Beginning at the right each figure in the subtrahend is subtracted from the figure about it and the individual remainder written below in the same column.
6. As a check the remainder and the subtrahend should be added.
7. If the subtraction was correct the sum of this addition will be equal to the minuend.

 

 

Ответ: 1, 4, 2, 5, 3, 6, 7.

 

II

 

1. When either of these is placed between any two numbers it indicates respectively that the sum, difference, product, or quotient of the two numbers is to be found.
2. Another sign sometimes used is the parentheses.
3. the equality sign shows that any indicated operation or combination of numbers written before it produces the result written after it.
4. The signs most used in arithmetic to indicate operations with numbers are the plus, minus, multiplication, and division signs. If any number oк combination of numbers is inclosed in parentheses the whole combinations, or the result of the indicated operations, inside the parentheses is to be considered as a single number.

 

Ответ: 4, 1, 3, 2, 5

 

 

III

1. Thus 6 is a divisor of 42, the quotient being 7.
2. A divisor has already been defined.
3. Also, 3 is a divisor of 42, the quotient being 14.
4. It is seen that a divisor is in reality a factor.
5. In the sense in which we shall use it in this chapter, however, a divisor of any number is another number which is contrained in that one a whole number of times, that is, exactly and without a remainder.
6. This was to be expected, since in division, the dividend is the product of the devisor and the quotient.

 

Ответ: 2, 5, 6, 4, 1, 3

 

 

Упражнение 10. Выберите правильный ответ

1. Write down the number which is 3 times as big (much) as a.	3a, 4-a, 5a
2. Write down the number which is 2 less than x.	x-2, 2x, x + 2
3. Find 2 consecutive integers whose sum is 39.	20 and 19, 19 and 1, 17 and 18.
4. Using the letters x and y, write the following: two numbers differ by 6 (note, y is greater than x)	y-x = 6, x – y = 6, y – x = 2
5. If a is a multiplier and и is the product, what is the multiplicand equal to?	a:b, a – b, b:a

 

 

Упражнение 11.

Ответьте правильно

 

1. What laws does the operation of addition obey?	1. There exists the law called the distributive connecting the operation of addition and multiplication.   2. There are two laws called the Commutative law and the Associative law holding good for addition.   3. The Commutative law, the Associative law and the Distributive law are the fundamental laws of arithmetic.
2. Is the remainder changed if one and the same number is added to the subtrahend and minuend?	1. The result of the operation of subtraction is the same, one and the same number being added to the subtrahend and the minuend.   2. Using the fundamental property of the difference we may add one and the same number to the subtrahend and minuend.   3. Any changes in the subtrahend yield the changing of the remainder.
3. What is required to find in dividing the number 8 by the number 2?	1. It is required to find such a number which is 2 units greater than the number 8.   2. It is required to find out how many times the number 2 is contained in the number 8.   3. It is required to find the number which being added to the number 2 gives the number 8.

 

 

Упражнение 12.

Выберите правильный вопрос

1. The equality sign shows that any indicated operation or combination of numbers written before it (on the left) produces the result or number written after it.	1. What sign is placed between the two results if the first gives the second?   2. What relation should be between the dividend and the divisor for the operation of division to be exact?   3. What fundamental operations in arithmetic do you know?
2. The signs most used in arithmetic to indicate operations with numbers are the plus, minus, multiplication, and division signs.	1. How many operations are there in arithmetic?   2. What signs indicating the arithmetical operations do you know?   3. What does the sign + placed between any two numbers indicate?
3. In finding the product of any two numbers which do not contain the same number of figures, the one with the lesser number of figures should be taken as the multiplier.	1. What operations should be performed over any two numbers if their product is to be found?   2. What rule do you follow to multiply two numbers having different number of digits?   3. What happens to the product, the multiplier decreasing several times?
4. The numbers to be added are called the addends.	1. What operation is performed over the numbers called the addends?   2. What do we call the numbers, if their combined amount is spoken of as the sum?   3. Is the sum changed if one of the addends increases?

 

Упражнение 13

Прочтите следующие утверждения, скажите, правильные они, неправильные или не включены в текст.

 

1. If a certain number is the product of two or more other numbers each of those other numbers is called a factor of that number. (T)

 

2. A divisor of any number is another number which is contained in that one a whole number of times, that is, exactly and without a remainder. (F, may be with a remainder)

 

3. The number 5 is a factor of the number 12. (F, we can’t divide 12 into 5, see 1)

 

4. We shall call number 2 and 3 and 4 and 6 proper factors of 12. (T)

 

5. A number which has the number 3 as a factor is called an even number. (F, not always, f.e. 9)

 

6. The integer "m” is a factor of the integer "n” if mg=n, where q is an integer. (T)

 

7. In general if "m” and "n” are positive integers and if "m” is a factor of "n”, we say that m divides n, or n is divisible by m. (T)

 

8. We shall say that 0 is divisible by every integer, but 0 does not divide any number. (T)

 

9. If any even number is divisible by 3 it is divisible by 8. (T)

 

10. If the number consisting of the last two figures of any given number is divisible by 4 or by 25, the entire number is divisible by 4 or 25, respectively. (T)

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